Here is a (slightly shortened) joke from the book The Curious Incident of The Dog in the Night-Time:

There are three men on a train. One of them is an economist and one of them is a logician and one of them is a mathematician.  And they have just crossed the border into Scotland and they see a brown cow standing in a field from the window of the train.

And the economist says, "Look, the cows in Scotland are brown."

And the logician says, "No. there are cows in Scotland of which one at least is brown."

And the mathematician says, "No. there is at least one cow in Scotland, of which one side appears to be brown."

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  • Gwern

    While we’re telling jokes…

    A farmer has three sons, an engineer, a physicist, and a mathematician. They return from college and he assigns them chores. One is to construct a fence enclosing as large an area as possible using 20ft of wood fencing.
    The engineer makes a 5x5x5x5 cube, and leaves, satisfied with his work.
    The physicist, with a grin, makes a circle with a diameter of 20ft, which obviously encloses more area than the engineer’s.
    The mathematician simply grabs some fencing, wraps it all around his body, and says:
    “I define myself as outside the fence.”

  • conchis

    “The engineer makes a 5x5x5x5 cube, and leaves, satisfied with his work. The physicist, with a grin, makes a circle with a diameter of 20ft, which obviously encloses more area than the engineer’s.”

    Eh? I assume you mean a 5×5 square (perimeter 5+5+5+5 = 20, area = 25) and a circle with circumference 20 (diameter = 20/pi, area = 100/pi)?

  • Nick Tarleton

    Assume a spherical brown Scottish cow…

  • Michael Sullivan

    The way I heard and tell the fence one, the engineer makes a circle, and the physicist waits for a very foggy day and extends the fence straight out in both directions, and then claims that the fence continues around the earth and encloses half of it.

    This version doesn’t have much respect for engineers. Not only are they not aware of the circle, but “cube, square, what’s the difference?” Not that my version is particularly friendly to physicists. I think mathematicians made up most of these jokes. Perhaps it’s only from my warped pure math perspective that it always feels like they “win”.

  • Doug S.

    The version I heard of the fence joke:

    An engineer, a physicist, and a mathematician are asked to enclose a group of sheep using the smallest amount of fence.

    The engineer reasons that a circle will enclose the most area for a given amount of fence, and then builds a circular fence around the sheep.

    The physicist builds a fence at infinity and then pulls it tight around the sheep, hoping to produce the smallest possible circular fence that contains all the sheep.

    The mathematician, meanwhile, builds a small fence around himself, and then shouts, “I declare myself to be on the outside!”

    Here’s another joke:

    A biologist, a physicist, and a mathematician are sitting on a bench facing the entrance to a building. They see two people enter the building, and then see three people leave.

    The biologist says, “They must have reproduced while they were inside.”

    The physicist says, “No, our initial observation must be in error.”

    The mathematician says, “If one more person goes inside, then the building will be empty.”

    I know more like these. Want to hear them?

    • ray gravitt

      I found this page looking for a joke much like these but with a philosopher,a mathematician and a logician who encounter sheep while riding a train in Scotland.They comment on the color,each observation being obviously limited by the constraints of their thought systems.Do you know that one?It is a teaching tool I wish my son to encounter.

  • anonymous

    An applied mathematician, a logician and a topologist are each locked in an otherwise empty room and given a can of beans. Their task is to open it.

    Their captor returns after a while to check on their progress.

    The applied mathematician has used brute force to open his can by cracking it against the bricks of the wall, and is happily eating the beans.

    The logician is still sitting there thinking about it.

    The topologist seems to have escaped, but his can of beans is wobbling and moving as if something inside it is struggling to get out. A little voice can be heard from within: “Help! I made a sign error!”

  • I usually tell the cow train joke with a computer scientist, an engineer, and a mathematician, which in my mind works best since a computer scientist just wants to get within an order, an engineer wants a realistic approximation and doesn’t mind if he is surprised very rarely, and a mathematician wants it precisely right. And, actually, I learned the joke this way in a computer science course because he wanted to make it clear to us the level of accuracy we were striving for in calculating the runtime of an algorithm.

  • Doug S.

    A mathematician, a physicist, and a lawyer were each asked to find the height of a tall building.

    The mathematician measures the length of the building’s shadow and the angle to the top of the building, then calculates “height = length*tan(angle)”.

    Meanwhile, the physicist goes to the roof of the building, drops a heavy weight over the side, measures how long it takes the weight to hit the ground, then calculates “height = (1/2)gt^2”.

    Finally, the lawyer goes inside, finds the office of the building superintendent, and asks him how tall the building is.

  • Gwern

    Ack, Conchis. You are correct! It was circumference of 20 ft and a 5×5 square (although I was actually thinking that each side is 5 ft, so 5x5x5x5 but I went one x5 too far and I am no longer sure that even makes sense). That’s what I sort of intended.

    I was obviously too sleepy at 2 AM or whatever to be posting anything about math. A lesson is learned but the damage is irreversible!

  • SunTzuWarmaster

    Here is a real life example for accountants, engineerings, and marketing majors at my Aunt Becky’s corperate baseball game:
    Everyone was given tickets to the baseball game.
    The accountants went into the stadium, looked at their tickets, found their seats, and sat down.
    The engineers went into the stadium, found their seats, waited for the game to start, and moved forward to fill the better, empty, seats.
    The accountants entered as a group, asked an usher where their seats were, gave him $50, and sat in the front row.

  • quintopia

    For especially nerdy people, I tell the fence joke where the goal is simply to enclose a fixed number of sheep with a minimal amount of fence. The engineer builds a circle and the physicist encloses the convex hull of the sheep with the sheep packed into as tight a circle as possible, thus saving a foot or so off the engineer’s design.

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